Scientific Project

Algorithmic Developments for Generalized Nash Equilibrium Problems with Applications

This project deals with investigation of solving methods for generalized Nash equilibrium problems (GNEP) with the applications.

Start Date:

01.12.2015

End Date:

28.02.2017

Faculty:

Faculty of Mathematics, Computer Science and Natural Sciences

Funded by:

Asian development bank, Higher Education Reform project, Ministry of Education, Culture, Science

Aim/Goal of the project

The main goal of the project is to investigate generalized Nash equilibrium problems with applications in order to obtain some theoretical and numerical results based on recent developments in non-smooth optimization.

Description of the project

This project deals with investigation of solving methods for generalized Nash equilibrium problems (GNEP). Since GNEP can be reduced into quasi-variational inequalities, it is also important to investigate both problems. Based on duality theory in convex optimization, we introduce gap functions for quasi-variational inequalities and by investigating properties of suggested functions, we investigate an algorithm for solving quasi-variational inequalities and consider applications to GNEP.

In order to develop a new algorithm for solving GNEP, we try to use recent developments in numerical methods for non-smooth optimization. Moreover, we concentrate on some applications of GNEP, specially in insurance market.

Expected outcomes  

  1. A new algorithm for solving variational inequalities based on the gap function approach via conjugate duality in convex optimization will be introduced.
  2. Relationships between the suggested algorithm and solving methods for GNEP will be investigated.
  3. An algorithm for GNEP by combining new developments in numerical methods for nonsmooth optimization will be developed.
  4. Some applications of GNEP to insurance and other fields will be investigated  and the obtained results with known ones will be compared.